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This is a substantially revised version of the first chapter of my Harvard University Ph.D. thesis, “Essays in Bimetallism and Early International Lending.” It has been submitted for publication in the Quarterly Journal of Economics. I would like to thank Michael Bordo, Milton Friedman, Peter Garber, Charles Kindleberger, John Leahy, Karen Lewis, Angela Redish, Matthew Shapiro, Jeff Williamson; and seminar participants at the Workshop on the History of International Monetary Arrangements at Arrabida, Portugal and at the Federal Reserve Board, Harvard University, NBER, the University of Michigan, Rutgers University, and the Wharton School for helpful discussions and comments. I am especially grateful to Greg Mankiw for exceptional guidance throughout the evolution of this paper. I am responsible for any remaining errors.
Full-bodied coins are coins with an intrinsic metal value equal to their face value, whereas token coins are coins with a face value higher than their intrinsic value. Redish (1990, 1992) discusses the importance of token coinage for the choice between a bimetallic and monometallic system. She argues that only after the technology became available to manufacture token coins that were difficult to counterfeit did a monometallic gold standard become feasible.
Kindleberger (1984) notes that Gresham’s Law was actually discovered two centuries earlier by Nicolas Oresme in 1360.
As I will show below, the risk of “realignment” is also absent, since the authorities have no incentive to change the mint ratio when Fisher’s arbitrage mechanism is operational.
This is the reason countries could maintain the widely different mint ratios depicted in Chart 4 without creating an opportunity for unlimited arbitrage. If the mints had taken it upon themselves to trade gold for silver at the fixed mint ratio, arbitrageurs could have in principle made unlimited profits. In the 1820s for example, anyone could then have bought gold at the U.S. mint and sold it at the Spanish mint for an immediate gross profit of 11 percent. Clearly, the U.S. mint would have run out of gold very quickly, while the Spanish mint would have run out of silver. This is why the mints were not in the business of fixing the market ratio.
Rolnick and Weber (1986) propose a much less universally valid version of Gresham’s Law in which Fisher’s mechanism might not operate: unless this would be prohibitively expensive—as in the case of small-denomination coins—undervalued coins would trade at a premium instead of being melted down. They offer anecdotal evidence that suggests the practice was widespread. Greenfield and Rockoff (1992) offer evidence to the contrary, however, and claim the traditional version of Gresham’s Law was generally valid. In any case, I will assume here that if coins trade at a premium, they have in effect been transferred to the bullion market. Under this assumption, the act of bimetallic arbitrage takes place when coins that previously traded at their face value trade at a premium for the first time.
Bimetallic arbitrage will not completely fix the market ratio. Because of costs connected to arbitrage, such as melting and minting costs, the ratio will fluctuate in a band around the bimetallic ratio. Arbitrage will not be profitable until the market ratio has moved a certain distance away from the bimetallic ratio. In analogy with gold points under a gold standard, I will call the points at which bimetallic arbitrage becomes profitable “gold-silver points.” It is not immediately clear how far these gold-silver points were from the mint ratio. The main part of the costs of arbitrage was seigniorage charged by the mint, since bimetallic arbitrage could be conducted entirely in domestic bullion markets, eliminating the need to ship the metals over long distances. The only other major costs were melting costs and the cost of trading gold for silver in the bullion market, which were most likely small. The seigniorage charged by the French mint amounted to 1.0 percent for silver and 0.19 percent for gold, so that the upper gold-silver point was probably close to 15.7 and the lower gold-silver point close to 15.4. This refers to the gold-silver points with respect to the market ratio prevailing in France, however. If we compare the French mint ratio with the market ratio in London, the gold-silver points would most likely be farther away from the mint ratio, since arbitrage between the French monetary system and the London bullion market does of course involve the shipping of bullion across the Channel.
In Oppers (1993) I discuss the anecdotal evidence and show how we can use data on the exchange rate of a bimetallic currency to determine the relative circulation of gold and silver in the money supply. As an example, the paper shows that by the end of the 1850s silver coins could no longer be obtained at face value in France. Either they had disappeared through arbitrage, or they had started to trade at a premium over gold coins. In either case, further bimetallic arbitrage was impossible.
The theory of stochastic process switching and target zones, developed by Flood and Garber (1983, 1991), Froot and Obstfeld (1991a, 1991b), Krugman (1991), and Smith (1991) has been used to model many phenomena. They include Britain’s return to gold in 1925 and entry in the EMS (Miller and Sutherland 1992), exchange rate behavior after the Louvre accord (Lewis 1990), the EMS as a target zone (Delgado and Dumas 1991 and Svensson 1992a), and a collapsing gold standard (Krugman and Rotemberg 1990 and 1992).
For simplicity, I am abstracting from the existence of gold points here. It is assumed that bimetallic arbitrage is costless.
“Free” coinage refers to the right to have precious metals coined on demand. Coinage is “gratuitous” if there is no charge for it, i.e., the weight of the coins received is equal to the weight of the bullion supplied to the mint.
This can be safely done since in this case the exchange rate between the two areas is fixed at the bimetallic mint ratio, so the price-level movements and the interest rate are equal in both areas by Equations 3 and 4.
This assumes that demand for precious metals for nonmonetary uses is constant, and the supply of precious metals is dependent exclusively on technological and environmental factors, such as mining technology and new discoveries of metal deposits. Thus, after allowing for (constant) nonmonetary demand, the impact of the supply of precious metals on the monetary system comes as a series of random shocks to the supply of monetary gold and silver. These assumptions are somewhat restrictive and do not allow for things like an extended relative excess of gold production over silver production, such as gold rushes. More complex processes for k—notably autoregressive ones—can be imagined, but these do not allow for the explicit analytical solutions arrived at by Krugman. See Miller and Weller (1989) for a discussion.
Note the difference with the traditional target zone model, where infinitesimal intervention is required to obtain the target zone effects. Because of the different nature of the boundary—a hybrid between an absorbing and reflecting barrier—the largest target-zone effects occur when a large initial rush of arbitrage takes place.
A quick back-of-the-envelope calculation shows that there is evidence that this might have been the relevant case for nineteenth century bimetallism. For the values of γ and σ used in Figure 2 and for plausible relative sizes of the gold area (GS, consisting of the United Kingdom and the United States), the silver area (SS), and France (BIM); λ for the smooth-pasting solution is between 0.9964 (GS=0.4, SS-0.5, BIM=0.1) and 0.9988 (GS=0.2, SS=0.6, BIM=0.2). So between 0.12 percent and 0.36 percent of the French money stock would have had to have been converted “instantaneously” when the market ratio reached the mint ratio. To see that this is plausible, realize that the total stock of coins in 1849 was at most 3 billion francs (total cumulative silver coinage since 1820). A 0.12 percent and 0.36 percent share of this would be 3.6 million and 10.8 million francs, respectively. Total gold coinage in France in 1850 amounted to 85 million francs, most of it associated with six weeks’ worth of arbitrage in response to the drop in the market ratio below the French mint ratio on November 22, 1850. That is around 14 million francs per week, or 3 million francs per working day, close to what is needed for the smooth-pasting outcome to prevail.
Notice that σ is equal to the standard deviation of the first differences of the fundamentals. During the period 1880 to 1885 the bimetallic system had been abandoned, so that the market ratio was equal to the fundamentals: x = w + k. σ can therefore directly be measured by looking at the variability of the market ratio.
The results are similar for different estimates of γ. The low estimate of Friedman and Schwartz, γ = -2.85, leads to x - f = -0.108 and (iG - iS = 0.24 percent, while the high estimate, γ = -11.84, leads to x - f = -0.226 and (iG - iS) = 0.12 percent.
The combination of two one-sided target zones is a concept introduced by Krugman and Rotemberg (1990, 1992) to model a collapsing gold standard. The application to bimetallism is especially interesting since, in contrast to the hypothetical case of a collapsing gold standard, it allows for empirical analysis of the model.
A fourth test that looks at the relationship between the fundamentals and the market ratio is omitted here, since data on fundamentals—basically the monetary supplies of gold and silver—could only be obtained on a yearly basis for the period 1851-73. During this period, target zone effects might be observed only over the years 1859-67, when Fisher’s mechanism was most likely not operative. This leaves us with too few datapoints to be informative.
For an indication of the accuracy of this procedure, I obtained a directly observable interest rate from the Prijscourant of 1845, the guilder “Belening” rate, and compared it with the interest rate implicit in the spread between the spot and forward guilder bills of exchange on Amsterdam that were traded in London and quoted in the Course of the Exchange. For the 102 usable observations, the correlation coefficient was 0.91. A regression of the implicit rate on the belening rate had an R2 of 83 percent, with a coefficient of 1.11 and a standard error of 0.10.